The prime factorization calculator will take any number and find its prime factors. Simply type the number into our tool and in no time you'll find the prime factorization. To understand the whole process, first you must get familiar with the concept of a prime number. Moving a step further, you should think for a while about the difference between prime factor and prime factorization.

Below, you'll find all the answers as well as concise information on how to find prime factorization and what a factor tree is.

What is a prime number?

To understand prime factorization, we need to start from the beginning - what is a prime number? A prime number is any number whose only factors are one and itself - in other words, it can't be formed by multiplying two smaller natural numbers. A key point to note is that there must be two different factors, so 1 is not a prime number since both factors of 1 are the same. For example, 5 is a prime number since the only factors of 5 are 1 and 5. 6 is not a prime as apart from 1 and 6, other factors exist - 2 and 3.

There are infinitely many primes and there's no simple formula to determine whether a number is a prime or not. That's why this prime factorization calculator is such a great, multi-purpose tool - you can use it as a prime number calculator as well!

What is a prime factor?

Prime factors are factors of a number that themselves are prime numbers. For example, suppose we want to get the factors of 20. That is, we want to know what whole numbers multiply to give you 20. We know that 1 * 20 = 20, 2 * 10 = 20 and 4 * 5 = 20. But notice that 20, 10 and 4 are not prime factors. The only prime factors of 20 are 2 and 5. You can also get these factors with the use of our factor calculator.

What is prime factorization?

Prime factorization is when we break a number down into factors that are only prime numbers. If we look at the above example with 20, the factors are 1, 2, 4, 5, 10, 20. The best place to start is to find at least one initial factor that is prime. Since 5 is prime, we can start with 4 * 5. Notice that 4 is not prime, so we break 4 down into 2 * 2. Since 2 is prime, the prime factorization of 20 is 2 * 2 * 5. Go ahead and check this result with our prime factorization calculator.

How to find prime factorization? A factor tree method

We'll show you step by step how to find prime factorization. We'll use the factor tree diagram which is an easy way to break down a number into its prime factors. Are you ready?

  1. Take a number. There's no point in picking the prime number, as the prime factorization will finish at this point. Let's choose 36.
  2. Factor it into any two numbers, prime or not. You may want to take the easiest splits, e.g., if your number is even, split it into 2 and the other number. 36 is even so that we can write it as 2 * 18.
  3. Start constructing the factor tree. Draw two branches splitting down from your original number.
factor tree example, 36 split into 2 and 18
  1. Factor the next line. If your number is a prime, leave it as it is. If it's not a prime number, repeat step 2.
factor tree example, 36 split into 2 and 18, 18 into 2 and 9
  1. Repeat the steps until you're left with only prime numbers.
factor tree example, 36 split into 2 and 18, 18 into 2 and 9, 9 into 3 and 3
  1. Write down the final prime factorization and prime factors.
full factor tree with leaves

Take all the "leaves" of your factor tree and multiply them together:

36 = 2 * 2 * 3 * 3

That's how we find prime factorization!

The prime factors of our original number 36 are 2 and 3. The same prime factor may occur more than once, and that's our case - both prime numbers appear twice in the prime factorization, which also can be expressed as:

36 = 2² * 3²

Of course, you should get the same result with a different factor tree splits, as e.g. here:

factor tree, alternative split

Greatest Common Factor

Prime factorization is the first step in finding the greatest common factor - the greatest factor of two or more numbers. The GCF is especially useful for simplifying fractions and solving equations using polynomials. For example, the greatest common factor between 6 and 20 is 2: prime factorization of the first number is 6 = 2 * 3, the latter may be expressed as 20 = 5 * 2 * 2, and the only number which appears in both prime factorizations is 2, indeed. If you want to calculate greatest common factor in a snap, use our greatest common factor calculator.

Least Common Multiple

The use of the prime factorization calculator is also useful in finding the least common multiple. The LCM is important when adding fractions with unlike denominators. The least common multiple is obtained when multiplying the higher powers of all factors between the two numbers. For example, the least common multiple between 6 and 20 is (2 * 2 * 3 * 5) = 60. The LCM may be found by hand or with use of the least common multiple calculator.

What is prime factorization of...

Notice the list of prime factorizations below, which can be checked using our prime factorization calculator.

  • Prime factorization of 2: it's a prime number!
  • Prime factorization of 3: it's a prime number!
  • Prime factorization of 4: 2 * 2
  • Prime factorization of 5: it's a prime number!
  • Prime factorization of 6: 2 * 3
  • Prime factorization of 7: it's a prime number!
  • Prime factorization of 8: 2 * 2 * 2
  • Prime factorization of 9: 3 * 3
  • Prime factorization of 10: 2 * 5
  • Prime factorization of 11: it's a prime number!
  • Prime factorization of 12: 2 * 2 * 3
  • Prime factorization of 13: it's a prime number!
  • Prime factorization of 14: 2 * 7
  • Prime factorization of 15: 3 * 5
  • Prime factorization of 16: 2 * 2 * 2 * 2
  • Prime factorization of 17: it's a prime number!
  • Prime factorization of 18: 2 * 3 * 3
  • Prime factorization of 19: it's a prime number!
  • Prime factorization of 20: 2 * 2 * 5
  • Prime factorization of 21: 3 * 7
  • Prime factorization of 22: 2 * 11
  • Prime factorization of 23: it's a prime number!
  • Prime factorization of 24: 2 * 2 * 2 * 3
  • Prime factorization of 25: 5 * 5
  • Prime factorization of 26: 2 * 13
  • Prime factorization of 27: 3 * 3 * 3
  • Prime factorization of 28: 2 * 2 * 7
  • Prime factorization of 29: it's a prime number!
  • Prime factorization of 30: 2 * 3 * 5
  • Prime factorization of 31: it's a prime number!
  • Prime factorization of 32: 2 * 2 * 2 * 2 * 2
  • Prime factorization of 33: 3 * 11
  • Prime factorization of 34: 2 * 17
  • Prime factorization of 35: 5 * 7
  • Prime factorization of 36: 2 * 2 * 3 * 3
  • Prime factorization of 37: it's a prime number!
  • Prime factorization of 38: 2 * 19
  • Prime factorization of 39: 3 * 13
  • Prime factorization of 40: 2 * 2 * 2 * 5
  • Prime factorization of 41: it's a prime number!
  • Prime factorization of 42: 2 * 3 * 7
  • Prime factorization of 43: it's a prime number!
  • Prime factorization of 44: 2 * 2 * 11
  • Prime factorization of 45: 3 * 3 * 5
  • Prime factorization of 46: 2 * 23
  • Prime factorization of 47: it's a prime number!
  • Prime factorization of 48: 2 * 2 * 2 * 2 * 3
  • Prime factorization of 49: 7 * 7
  • Prime factorization of 50: 2 * 5 * 5
  • Prime factorization of 51: 3 * 17
  • Prime factorization of 52: 2 * 2 * 13
  • Prime factorization of 53: it's a prime number!
  • Prime factorization of 54: 2 * 3 * 3 * 3
  • Prime factorization of 55: 5 * 11
  • Prime factorization of 56: 2 * 2 * 2 * 7
  • Prime factorization of 57: 3 * 19
  • Prime factorization of 58: 2 * 29
  • Prime factorization of 59: it's a prime number!
  • Prime factorization of 60: 2 * 2 * 3 * 5
  • Prime factorization of 61: it's a prime number!
  • Prime factorization of 62: 2 * 31
  • Prime factorization of 63: 3 * 3 * 7
  • Prime factorization of 64: 2 * 2 * 2 * 2 * 2 * 2
  • Prime factorization of 65: 5 * 13
  • Prime factorization of 66: 2 * 3 * 11
  • Prime factorization of 67: it's a prime number!
  • Prime factorization of 68: 2 * 2 * 17
  • Prime factorization of 69: 3 * 23
  • Prime factorization of 70: 2 * 5 * 7
  • Prime factorization of 71: it's a prime number!
  • Prime factorization of 72: 2 * 2 * 2 * 3 * 3
  • Prime factorization of 73: it's a prime number!
  • Prime factorization of 74: 2 * 37
  • Prime factorization of 75: 3 * 5 * 5
  • Prime factorization of 76: 2 * 2 * 19
  • Prime factorization of 77: 7 * 11
  • Prime factorization of 78: 2 * 3 * 13
  • Prime factorization of 79: it's a prime number!
  • Prime factorization of 80: 2 * 2 * 2 * 2 * 5
  • Prime factorization of 81: 3 * 3 * 3 * 3
  • Prime factorization of 82: 2 * 41
  • Prime factorization of 83: it's a prime number!
  • Prime factorization of 84: 2 * 2 * 3 * 7
  • Prime factorization of 85: 5 * 17
  • Prime factorization of 86: 2 * 43
  • Prime factorization of 87: 3 * 29
  • Prime factorization of 88: 2 * 2 * 2 * 11
  • Prime factorization of 89: it's a prime number!
  • Prime factorization of 90: 2 * 3 * 3 * 5
  • Prime factorization of 91: 7 * 13
  • Prime factorization of 92: 2 * 2 * 23
  • Prime factorization of 93: 3 * 31
  • Prime factorization of 94: 2 * 47
  • Prime factorization of 95: 5 * 19
  • Prime factorization of 96: 2 * 2 * 2 * 2 * 2 * 3
  • Prime factorization of 97: it's a prime number!
  • Prime factorization of 98: 2 * 7 * 7
  • Prime factorization of 99: 3 * 3 * 11
  • Prime factorization of 100: 2 * 2 * 5 * 5
  • Prime factorization of 104: 2 * 2 * 2 * 13
  • Prime factorization of 105: 3 * 5 * 7
  • Prime factorization of 108: 2 * 2 * 3 * 3 * 3
  • Prime factorization of 117: 3 * 3 * 13
  • Prime factorization of 120: 2 * 2 * 2 * 3 * 5
  • Prime factorization of 121: 11 * 11
  • Prime factorization of 125: 5 * 5 * 5
  • Prime factorization of 126: 2 * 3 * 3 * 7
  • Prime factorization of 130: 2 * 5 * 13
  • Prime factorization of 132: 2 * 2 * 3 * 11
  • Prime factorization of 135: 3 * 3 * 3 * 5
  • Prime factorization of 140: 2 * 2 * 5 * 7
  • Prime factorization of 144: 2 * 2 * 2 * 2 * 3 * 3
  • Prime factorization of 147: 3 * 7 * 7
  • Prime factorization of 150: 2 * 3 * 5 * 5
  • Prime factorization of 162: 2 * 3 * 3 * 3 * 3
  • Prime factorization of 175: 5 * 5 * 7
  • Prime factorization of 180: 2 * 2 * 3 * 3 * 5
  • Prime factorization of 196: 2 * 2 * 7 * 7
  • Prime factorization of 200: 2 * 2 * 2 * 5 * 5
  • Prime factorization of 210: 2 * 3 * 5 * 7
  • Prime factorization of 216: 2 * 2 * 2 * 3 * 3 * 3
  • Prime factorization of 225: 3 * 3 * 5 * 5
  • Prime factorization of 245: 5 * 7 * 7
  • Prime factorization of 250: 2 * 5 * 5 * 5
  • Prime factorization of 256: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
  • Prime factorization of 300: 2 * 2 * 3 * 5 * 5
  • Prime factorization of 375: 3 * 5 * 5 * 5
  • Prime factorization of 400: 2 * 2 * 2 * 2 * 5 * 5
  • Prime factorization of 500: 2 * 2 * 5 * 5 * 5
  • Prime factorization of 625: 5 * 5 * 5 * 5

At the beginning, 1 was considered a prime number. It was not until the early 20th century that most mathematicians excluded 1 as a prime number. Notice the prime factorization calculator does not include 1 in the results of prime numbers.

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Prime Factorization. Calculator | Definition | Factor tree